function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
%   taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);


for iter = 1:num_iters

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta. 
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
    %

temp0 = theta(1,1) - (alpha * (1/m * (sum((X * theta) - y))));
temp1 = theta(2,1) - (alpha * (1/m * sum(((X * theta) - y) .* X(:,2))));
theta(1,1) = temp0;
theta(2,1) = temp1;
%fprintf('theta 0 = %f\n', temp0);
%fprintf('theta 1 = %f\n', temp1);

    % ============================================================

    % Save the cost J in every iteration    
    J_history(iter) = computeCost(X, y, theta);
    %fprintf('J value = %f\n', J_history(iter));
    %fprintf('\n');
end

end
